🧮 algebra

1. The problem is to solve the equation given (though no explicit equation was provided, we assume a general approach to solving algebraic equations). 2. To solve an algebraic equa

1. ปัญหาข้อ 25: \(2^{x+y} = 6^{y}\) และ \(3^{x-1} = 2^{y+1}\) 2. เริ่มจากเขียนสมการทั้งสองในรูปที่ใช้ฐานเดียวกันหรือแปลงให้ง่ายขึ้น

1. **State the problem:** We need to find the 10th term of a geometric sequence where the first term $a_1 = -5$ and the common ratio $r = -2$. 2. **Formula for the $n^{th}$ term of

1. **State the problem:** We need to find the sum of all terms in a geometric series where the first term $a_1=4$ and the second term $a_2=-3$. 2. **Recall the formula for the sum

1. **State the problem:** Find the 10th term of a geometric sequence where the 1st term $a_1 = -3$ and the 4th term $a_4 = 81$. 2. **Recall the formula for the $n$th term of a geom

1. **State the problem:** Calculate the sum of the first 6 terms of a geometric series with first term $a_1 = -21$ and common ratio $r = -\frac{2}{3}$. 2. **Formula for sum of firs

1. **State the problem:** We need to find the sum of the first 12 terms of a geometric series where the first term $a_1 = -3$ and the second term $a_2 = 6$. 2. **Find the common ra

1. The problem is to convert mixed numbers to improper fractions. 2. The formula to convert a mixed number $a \frac{b}{c}$ to an improper fraction is:

1. **State the problem:** We have a geometric sequence where the first term $a_1 = 6$ and the second term $a_2 = 18$. We need to find the 8th term $a_8$. 2. **Recall the formula fo

1. **Problem:** Given vectors $a = \left(-7, -15\right)$ and $b = \left(10, 16\right)$, find $8\left(a + \frac{1}{2}b\right)$. 2. **Formula and rules:** To solve this, we use vecto

1. Let's create a simple linear equation that is easy to fit on a cue card. 2. A linear equation has the form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept.

1. **State the problem:** Calculate $\left(7 \frac{5}{12} - 5 \frac{3}{4}\right) \div 2^{2 \frac{1}{2}}$. 2. **Convert mixed numbers to improper fractions:**

1. **Problem:** Given $a = -7i$ and $b = \frac{1}{6}i$, find $8(a + 2b)$. 2. **Formula and rules:** To solve this, use the distributive property and combine like terms. Remember th

1. **State the problem:** We need to add the fractions $\frac{1}{3}$ and $\frac{1}{4}$. 2. **Formula and rules:** To add fractions, they must have a common denominator. The formula

1. **State the problem:** Solve the equation $7(2k+1) = 3(4k-2)$ for $k$. 2. **Apply the distributive property:** Multiply out both sides:

1. The problem is to evaluate the expression $10|\sqrt{200}$, where $10$ is outside the square root and $\sqrt{200}$ is inside the root. 2. First, simplify the square root $\sqrt{2

1. Masalah: Tentukan asimtot dari fungsi yang diberikan. 2. Asimtot adalah garis yang mendekati grafik fungsi saat variabel mendekati nilai tertentu (biasanya tak hingga atau titik

1. **State the problem:** Solve the quadratic equation $$x^2 + x - 56 = 0$$. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by

1. **State the problem:** Calculate the final price of a shirt originally priced at 80 with a 20% discount, then an additional 10% coupon discount on the sale price, and finally a

1. Diketahui fungsi $y = \log(x+1)$. Kita diminta menentukan domain fungsi, asimtotnya, dan grafik serta pergeseran dari grafik $y = \log x$. 2. Domain fungsi logaritma $y = \log(x

1. Let's start with Quadratic Equations and their roots and discriminant. A quadratic equation is of the form $$ax^2 + bx + c = 0$$ where $a \neq 0$.